Three weak solutions for degenerate weighted quasilinear elliptic equations with indefinite weights and variable exponents
This paper explores the multiplicity of weak solutions to a class of weighted elliptic problems with variable exponents, incorporating a Hardy term and a nonlinear indefinite source term. Using critical point theory applied to the associated energy functional, we establish the existence of at least...
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| Format: | Article |
| Language: | English |
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AIMS Press
2025-02-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2025207 |
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| author | Khaled Kefi Nasser S. Albalawi |
| author_facet | Khaled Kefi Nasser S. Albalawi |
| author_sort | Khaled Kefi |
| collection | DOAJ |
| description | This paper explores the multiplicity of weak solutions to a class of weighted elliptic problems with variable exponents, incorporating a Hardy term and a nonlinear indefinite source term. Using critical point theory applied to the associated energy functional, we establish the existence of at least three weak solutions under general assumptions on the weight function and the nonlinearity. This result has wide applicability, extending existing theories on quasilinear elliptic equations. |
| format | Article |
| id | doaj-art-74c8a2941ac64382be4736d3e17a4ace |
| institution | OA Journals |
| issn | 2473-6988 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-74c8a2941ac64382be4736d3e17a4ace2025-08-20T01:54:41ZengAIMS PressAIMS Mathematics2473-69882025-02-011024492450310.3934/math.2025207Three weak solutions for degenerate weighted quasilinear elliptic equations with indefinite weights and variable exponentsKhaled Kefi0Nasser S. Albalawi1Center for Scientific Research and Entrepreneurship, Northern Border University, Arar 73213, Saudi ArabiaDepartment of Computer Sciences, Faculty of Computing and Information Technology, Northern Border University, Rafha, Saudi ArabiaThis paper explores the multiplicity of weak solutions to a class of weighted elliptic problems with variable exponents, incorporating a Hardy term and a nonlinear indefinite source term. Using critical point theory applied to the associated energy functional, we establish the existence of at least three weak solutions under general assumptions on the weight function and the nonlinearity. This result has wide applicability, extending existing theories on quasilinear elliptic equations.https://www.aimspress.com/article/doi/10.3934/math.2025207variational methodshardy inequalitydegenerate $ p(x) $-laplacian operators |
| spellingShingle | Khaled Kefi Nasser S. Albalawi Three weak solutions for degenerate weighted quasilinear elliptic equations with indefinite weights and variable exponents AIMS Mathematics variational methods hardy inequality degenerate $ p(x) $-laplacian operators |
| title | Three weak solutions for degenerate weighted quasilinear elliptic equations with indefinite weights and variable exponents |
| title_full | Three weak solutions for degenerate weighted quasilinear elliptic equations with indefinite weights and variable exponents |
| title_fullStr | Three weak solutions for degenerate weighted quasilinear elliptic equations with indefinite weights and variable exponents |
| title_full_unstemmed | Three weak solutions for degenerate weighted quasilinear elliptic equations with indefinite weights and variable exponents |
| title_short | Three weak solutions for degenerate weighted quasilinear elliptic equations with indefinite weights and variable exponents |
| title_sort | three weak solutions for degenerate weighted quasilinear elliptic equations with indefinite weights and variable exponents |
| topic | variational methods hardy inequality degenerate $ p(x) $-laplacian operators |
| url | https://www.aimspress.com/article/doi/10.3934/math.2025207 |
| work_keys_str_mv | AT khaledkefi threeweaksolutionsfordegenerateweightedquasilinearellipticequationswithindefiniteweightsandvariableexponents AT nassersalbalawi threeweaksolutionsfordegenerateweightedquasilinearellipticequationswithindefiniteweightsandvariableexponents |